The curse of dimensionality in high-dimensional optimization: It is inherently seen that the dimensionality of feature space presents a fundamental challenge to high-dimensional optimization: as dimensionality increases, feature space becomes computationally inefficient, overfitted and model interpretability declines, thus requiring highly robust sparsity-based solutions. To find a solution to these problems, a new quantum-inspired framework of sparse optimization is proposed in this study, which combines probabilistic Q-bit representation and L1-regularized optimization to efficiently consider large solution spaces but with a sparsity constraint. The suggested method builds on quantum-inspired search algorithms such as initiation by superposition and rotation gate updates to the search to improved exploration and exploitation ratio, leading to a better convergence process. Experimental analyses show that the framework produces better optimization accuracy, indicated by much lower Mean Squared Error (MSE) and convergence rates than classical and met heuristic baselines, with the framework also having a higher level of sparsity in the solution space. These results highlight the effectiveness of the proposed method in handling high-dimensional problems, making it particularly suitable for applications in signal processing, machine learning-based feature selection, and large-scale scientific computing tasks.
The curse of dimensionality in high-dimensional optimization: It is inherently seen that the dimensionality of feature space presents a fundamental challenge to high-dimensional optimization: as dimensionality increases, feature space becomes computationally inefficient, overfitted and model interpretability declines, thus requiring highly robust sparsity-based solutions. To find a solution to these problems, a new quantum-inspired framework of sparse optimization is proposed in this study, which combines probabilistic Q-bit representation and L1-regularized optimization to efficiently consider large solution spaces but with a sparsity constraint. The suggested method builds on quantum-inspired search algorithms such as initiation by superposition and rotation gate updates to the search to improved exploration and exploitation ratio, leading to a better convergence process. Experimental analyses show that the framework produces better optimization accuracy, indicated by much lower Mean Squared Error (MSE) and convergence rates than classical and met heuristic baselines, with the framework also having a higher level of sparsity in the solution space. These results highlight the effectiveness of the proposed method in handling high-dimensional problems, making it particularly suitable for applications in signal processing, machine learning-based feature selection, and large-scale scientific computing tasks.
High-dimensional data presents significant challenges to traditional clustering algorithms due to the "curse of dimensionality," leading to sparsity issues, increased computational complexity, and reduced cluster quality. This research investigates the application of quantum-inspired algorithms to enhance clustering performance in these scenarios. We propose a novel clustering framework leveraging concepts from quantum annealing and quantum walks to efficiently explore the feature space and identify clusters. The core idea is to mimic the probabilistic and superposition properties of quantum systems within the clustering process, allowing for more nuanced exploration of potential cluster configurations. The algorithms are designed to mitigate the effects of dimensionality by introducing stochastic search strategies and exploiting correlations between features. We evaluate the effectiveness of these algorithms on benchmark datasets, demonstrating improved clustering accuracy and reduced computational cost compared to established classical methods. The research highlights the potential of quantum-inspired approaches as a viable solution for high-dimensional clustering problems.
Bayesian optimization has emerged as a powerful technique for tackling high-dimensional black-box optimization problems. However, its performance often degrades significantly when the dimensionality of the search space increases, a phenomenon known as the "curse of dimensionality." This paper proposes a novel approach – Quantum-Inspired Bayesian Optimization – that addresses this limitation by incorporating principles inspired by quantum computing, specifically quantum annealing. The core idea is to utilize a modified version of quantum annealing to guide the acquisition of function evaluations, exploiting superposition and interference to enhance exploration in high-dimensional spaces. We formulate the optimization problem as a quantum-inspired search, where candidate solutions exist in a superposition of states and are refined through interference effects. The algorithm iteratively updates the probability distribution over the search space, favoring regions with high potential based on the quantum-inspired exploration strategy. We demonstrate the effectiveness of this approach through theoretical analysis and illustrate its potential through conceptual examples, highlighting its ability to mitigate the curse of dimensionality and improve optimization performance compared to traditional Bayesian optimization methods. The key contributions of this work include the formalization of the quantum-inspired Bayesian optimization framework, the design of the modified quantum annealing algorithm for Bayesian optimization, and the theoretical justification for its improved exploration capabilities.
The rapid growth of machine learning (ML) has been accompanied by a significant challenge: the scaling of optimization algorithms to handle the immense parameter spaces of modern models, such as deep neural networks. Traditional optimization methods, including gradient descent and its variants, often encounter difficulties in efficiently exploring these spaces, leading to slow training times and potential stagnation. This paper investigates the application of quantum-inspired optimization techniques to address this scaling problem. We explore algorithms inspired by quantum annealing and other quantum phenomena, adapting their core principles to classical computation. Specifically, we propose a novel optimization framework utilizing a stochastic search strategy based on quantum superposition and measurement, designed to navigate high-dimensional parameter spaces more effectively. The efficacy of this approach is evaluated through theoretical analysis and conceptual simulations, demonstrating its potential to accelerate the training of large-scale machine learning models. We demonstrate how these methods can improve convergence speed and potentially escape local minima more effectively than conventional techniques. The core contribution lies in providing a theoretical foundation and a practical framework for applying quantum-inspired concepts to optimization within the context of machine learning.
High dimensional data in machine learning (ML) however is not yet fully tapped due curse of dimensionality, sensitivity to local minima and computational burden. In this paper, we will introduce and test a new QIGS algorithm for such problems on classical computer. The efficiency of QIGS is demonstrated to be benefiting from the amplitude–phase hybrid probabilistic encoding and gradient-assisted update for optimizing entangling operations, which can effectively balance global exploration and local exploitation. We test this experiment on synthetic benchmark functions (Rastrigin, Rosenbrock, Ackley up to 5,000 dimensions) and real-world data sets (genomic profiles with 20,531 features and BERT-based sentiment embeddings with 768 features). It is also shown that QIGS achieves a classification accuracy of 94.2% on the genomic data (Adam: 91.5%, SGD: 90.7%, PSO: 89.8%) and reduces the number of iterations for convergence by 35–40% compared to fastest baseline on synthetic benchmarks. In addition, on the BERT representations QIGS got a training loss of 0.083 in 120 iterations (vs Adam's loss of 0.091 in 180 iterations). These results establish that QIGS is not only a faster converging algorithm, but also one which produces solutions of higher quality for many problems, thereby making it an accessible segue between classical optimization and the future of quantum-inspired machine learning.
Large-scale optimization problems, prevalent in diverse fields such as machine learning, logistics, and engineering design, pose significant challenges to classical optimization algorithms. These algorithms often suffer from slow convergence rates, premature convergence, and difficulty in exploring complex solution spaces. This paper explores the application of quantum-inspired search algorithms to address these limitations. We introduce a novel approach that draws inspiration from quantum measurement theory, specifically superposition and interference, to enhance the exploration capabilities of classical optimization techniques. The core idea is to mimic the probabilistic nature of quantum measurements to navigate the solution space more effectively. This approach allows for a more efficient exploration of potential solutions, leading to improved convergence rates and the ability to tackle larger and more complex problems. The algorithms presented are designed to be implementable within standard computational environments without requiring specialized quantum hardware. The performance of these algorithms is evaluated through simulations, demonstrating their potential to outperform traditional optimization methods in specific scenarios.
Stochastic Gradient Descent (SGD) is a cornerstone algorithm in training machine learning models, particularly deep neural networks. However, its performance degrades significantly as the dimensionality of the problem increases, a phenomenon known as the "curse of dimensionality." This paper introduces a novel optimization algorithm, Quantum-Inspired Stochastic Gradient Descent (QISGD), designed to mitigate this issue. QISGD draws inspiration from quantum mechanics, specifically the concepts of superposition and interference, to guide the stochastic updates. The algorithm utilizes a probability distribution that mimics a quantum state, enabling it to explore the loss landscape more effectively and potentially achieve faster convergence in high-dimensional spaces. We present a theoretical framework for QISGD and discuss its key components, including the initialization of the quantum state, the generation of stochastic updates, and the implementation of interference effects. The core idea is to treat the parameters of the model as a quantum state, allowing for a more nuanced exploration of the loss function. We analyze the algorithm's convergence properties and provide insights into its potential advantages over traditional SGD. The primary goal is to demonstrate that quantum-inspired techniques can provide a robust and efficient solution for high-dimensional optimization problems.